• East Asian mathematical journal
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• v.33 no.5
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• pp.511-525
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• 2017

We introduce an extrapolated higher order characteristic finite element method to construct approximate solutions of a Sobolev equation with a convection term. The higher order of convergence in both the temporal direction and the spatial direction in $L^2$ normed space is established and some computational results to support our theoretical results are presented.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.59-74
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• 2010

In this paper, we obtain the existence of positive solutions for a quasi-linear four-point boundary value problem of higher-order differential equation. By using the fixed point index theorem and imposing some conditions on f, the existence of positive solutions to a higher-order four-point boundary value problem with a p-Laplacian is obtained.

• Honam Mathematical Journal
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• v.26 no.4
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• pp.549-557
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• 2004

In this paper, we prove the product property and the existence of an extremal analytic disc relative to the higher order Kobayashi metric. Also by making use of the upper semicontinuity of the higher order Kobayashi metric, we introduce a pseudodistance and investigate some properties of that pseudodistance related to the usual Kobayashi metric.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.113-120
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• 2017

In this paper, we introduce degenerate tangent numbers ${\mathcal{T}}^{(k)}_{n,q}({\lambda})$ and tangent polynomials ${\mathcal{T}}^{(k)}_{n,q}(x,{\lambda})$ of higher order. Finally, we obtain interesting properties of these numbers and polynomials.

• Water for future
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• v.21 no.2
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• pp.193-201
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• 1988

A simplified model for higher order scanning curves in the soil water characteristic function is suggested. The conceptual hysteresis models developed by $Mualem_{8,9}$ are simplied for higher order scanning curves. Higher order drying curves are regarded as primary drying curves and the last wetting reversal point is assumed to be on the main wetting curve by moving that point vertically downward. For the higher order wetting curves, it is assumed that these curves can be regarded as primary curves and the last wetting reversal point sits on the imaginary main drying curve which passes through the last wetting reversal point. The water content computed from the simplified model are compared with those obtained from Mualem's original model for second order scanning curves. It is found that absolute differences between the two methods aree relatively small and the simplified model always underestimates for higher order drying curves while it overestimates for higher order wetting curves. Hence, those two tend to compensate each other for repeated drying-wetting processes. The simplified model approximates higher order scanning curves well and reduces computation considerably.

• Journal of IKEEE
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• v.24 no.4
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• pp.950-953
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• 2020

A switching differentiator that can estimate the 1st-order time-derivative of a time-varying signal was proposed, and it is extended later to the higher-order switching differentiator(HOSD) that can observe higher-order time-derivatives of a time-varying signal in previous works. By using HOSD, higher-order time-derivatives can be estimated without peaking or chattering, and it has an asymptotic tracking performance. However, there exist many design constants to be determined in HOSD. In this paper, a method of reducing the number of design constants is proposed to solve the problem. Simulations reveal the effectiveness of the proposed method.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.963-982
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• 2013

The Galerkin method has been developed mainly for 2nd order differential equations. To get numerical solutions, there are some choices of Riesz bases for the approximation subspace $V_j{\subset}L^2$. In this paper we shall propose a uniform approach to find suitable Riesz bases for higher order differential equations. Especially for the beam equation (4-th order equation), we also report numerical results.

• Journal of the Society of Naval Architects of Korea
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• v.29 no.4
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• pp.58-65
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• 1992

In this paper, wave resistance for a submerged body is calculated by a higher order panel method. The Neumann-Kelvin problem is solved by the source or normal dipole distribution method. The body surface is represented by a bicubic B-spline and the singularity strengths are approximated by a bilinear form. The results calculated by the higher order panel method are compared with those by the lowest order panel method developed by Hess & Smith. The convergence rate of the higher order panel method is much better than the lowest order panel method. But the wave resistance calculated by the higher order panel method still shows discrepancy with an analytic solution at low Froude number like that by the lowest order panel method.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.405-423
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• 2008

By using critical point theorem, we study a higher order difference system, and obtain some new sufficient conditions ensuring the existence of periodic solutions for such a system.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1539-1549
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• 2014

The closed spacelike hypersurfaces with higher order mean curvature is discussed in a de Sitter space. The hypersurface is proved stable if and only if it is totally umbilical.